Open-ended (extended/constructed) response questions as predictors of success on subsequent state mathematics examination: The influence of mathematical awareness and conceptual knowledge

Abstract

This study investigated the predictive ability of students’ responses to open-ended, constructed/extended questions in third and fourth grade mathematics content subcategories on subsequent fifth grade mathematics achievement proficiency levels. Open-ended, extended/constructed response questions reflected content as outlined by the National Council of Teachers of Mathematics (2007) in Statistics and Probability, Number Sense, Numeration and Operations, Geometry, Algebra, and Measurement. Archival data from over 300 third, fourth and fifth grade students in one public school in New York State during the 2003- 2009 academic school years were utilized. Predictor variables included Statistics and Probability, Number Sense, Numeration and Operations, Geometry, and Algebra in grades 3 and 4, and Measurement in grade 4.

Results of a statistical discriminant function analysis indicated that, overall, open-ended response question predict fifth grade proficient/non-proficient outcome levels. There was a variation in the predictability of these types of response questions based on grade level and item content specific subscale. At grade three, the variables of statistics and probability and geometry contributed most to overall fifth grade outcomes. In fourth grade, Number Sense, Numeration and Operations as well as Algebra contributed significantly to overall fifth grade achievement. This study adds to current literature investigating the importance of open-ended/constructed response questions and their use in mathematics education. It provides evidence that the constructed response question is an important predictor of and possible contributor to student outcomes on achievement tests in mathematics.

The study has possible implications in several areas. First, it submits that if open-ended response questions predict performance on students’ future mathematics achievement then educators should consider how this type of format can be used to support student mathematical knowledge, including using open-ended constructed response questions for incorporating formative assessment as well as changes in instructional design of mathematics curriculum. Second, future research should consider investigating the extent to which work with extended response type of activities contribute to greater understanding and higher performance in mathematics so that students will acquire mathematical understanding and awareness. Finally, these results contribute to the field of assessment by documenting the value of open-ended responses items on student overall achievement in mathematics.